# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/ADD__MODULUS_c0', ch4s_arithmetics_ADDu_u_MODULUSu_c0)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/ADD__MODULUS_c0', aHLu_FALSITY)).
fof(21, axiom,![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>![X12]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/ADD__MODULUS_c0', ah4s_arithmetics_MODu_u_PLUS)).
fof(22, axiom,![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>![X13]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/ADD__MODULUS_c0', ah4s_arithmetics_MODu_u_MOD)).
fof(23, axiom,![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/ADD__MODULUS_c0', ah4s_arithmetics_DIVMODu_u_ID)).
fof(24, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,X14),file('i/f/arithmetic/ADD__MODULUS_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(25, axiom,![X2]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X14))),file('i/f/arithmetic/ADD__MODULUS_c0', ah4s_arithmetics_ADDu_u_SYM)).
fof(26, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/ADD__MODULUS_c0', aHLu_BOOLu_CASES)).
fof(27, axiom,p(s(t_bool,t)),file('i/f/arithmetic/ADD__MODULUS_c0', aHLu_TRUTH)).
fof(29, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/arithmetic/ADD__MODULUS_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
